Textbook Problem

Continuing Problem 6, suppose the company is selling in the United States, the United Kingdom, and Japan. Assume the unit production cost is $50, and the exchange rates are 1.22 ($/£) and 0.00965 ($/¥). Each country has its own constant elasticity demand function. The parameters for the United States are 19,200,000 and −2; the parameters for the United Kingdom are 10,933,620 and −2.2; and the parameters for Japan are 15,003,380,400 and −1.9.

The company has a production capacity of 3000. Therefore, the company can sell only as many units, in total, to all three countries as it can produce.

1. a. Develop a spreadsheet model that determines the prices the company should charge and the numbers of units it should sell in each of the three countries to maximize its total profit in dollars. (Note that if total demand is greater than capacity, the company has to decide how much to sell in each country. Therefore, the amounts to sell become decision variables.)
2. b. When the capacity is 3000, is all of this capacity used? Answer the same question if the capacity is increased to 4000.
3. c. Discuss the customer behavior that might result from the solution to the model in part a. If the company sets its price in one country relatively low compared to its price in another country, what might customers do?

7.2 Pricing with Exchange Rate Considerations At Madison

We continue Example 7.1 but now assume that Madison manufactures its product in the United States and sells it in the United Kingdom (UK). Given the prevailing exchange rate in dollars per pound. Madison wants to determine the price in pounds it should charge in the UK so that its profit in dollars is maximized. The company also wants to see how the optimal price and the optimal profit depend on exchange rate fluctuations.

7.1 Pricing Decisions at Madison

The Madison Company manufactures and retails a certain product. The company wants to determine the price that maximizes its profit from this product. The unit cost of producing and marketing the product is $50. Madison will certainly charge at least $50 for the product to ensure that it makes some profit. However, there is a very competitive market for this product, so that Madison’s demand falls sharply when it increases its price. How should the company proceed?²

In the exchange rate model in Example 7.2, suppose the company continues to manufacture its product in the United States, but now it sells its product in the United States, the United Kingdom, and possibly other countries. The company can independently set its price in each country where it sells. For example, the price could be $150 in the United States and £110 in the United Kingdom. You can assume that the demand function in each country is of the constant elasticity form, each with its own parameters. The question is whether the company can use Solver independently in each country to find the optimal price in this country. (You should be able to answer this question without actually running any Solver model(s), but you might want to experiment, just to verify your reasoning.)